Let E be a Banach lattice and let M be a norm-closed and Dedekind σ-complete ideal of E. If E contains a lattice-isometric copy of ∞ , then E/M contains such a copy as well, or M contains a lattice copy of ∞. This is one of the consequences of more general results presented in this paper. 1. Introduction. Let E be a locally solid linear lattice (Riesz space), for example , a Banach lattice, let...

The present paper is concerned with some representatons of linear mappings of continuous functions into locally convex vector spaces, namely Theorem. If X is a complete Hausdorff locally convex vector space, then a general form of weakly compact mapping T : C[a, b] → X is of the form Tg = ∫ b a g(t)dx(t), where the function x(·) : [a, b] → X has a weakly compact semivariation on [a, b]. This th...

In this paper‎, ‎using the discrete Fourier transform in the finite-dimensional Hilbert space C^n‎, ‎a class of nonRieszable equal norm tight frames is introduced ‎and‎ using this class, a bound for Fiechtinger Conjecture is presented. By the Fiechtinger Conjecture that has been proved recently, for given A,C>0 there exists a universal constant delta>0 independent of $n$ such that every C-equal...

A particular notion of limit is introduced, for Riesz space-valued functions. The definition depends on certain ideals of subsets of the domain. It is shown that, according with our definition, every bounded function with values in a Dedekind complete Riesz space admits limit with respect to any maximal ideal. Mathematics Subject Classification (2000). Primary 28B15; Secondary 46G10.

A convergence in Riesz spaces is given axiomatically. A Bochner-type integral for Riesz space-valued functions is introduced and some Vitali and Lebesgue dominated convergence theorems are proved. Some properties and examples are investigated. A.M.S. SUBJECT CLASSIFICATION (2000): 28B15.

On the Euclidean space, it is well known that the Riesz transform has also a bounded extension L(M) → L(M ;TM) for any p ∈]1,∞[. However, this is not a general feature of the Riesz transform on complete Riemannian manifolds, as the matter of fact, on the connected sum of two copies of the Euclidean space R , the Riesz transform is not bounded on L for any p ∈ [n,∞[∩]2,∞[ ([9, 7]). It is of inte...

We construct a homeomorphism between the compact regular locale of integrals on a Riesz space and the locale of (valuations) on its spectrum. In fact, we construct two geometric theories and show that they are biinterpretable. The constructions are elementary and mostly consist of explicit manipulations on a distributive lattice associated to a given Riesz space.

This paper is concerned with the numerical solutions of a variable-order space-time fractional reaction-diffusion model. The space-time fractional derivative is considered in the sense of Riesz-Feller, the system is defined by replacing the second order space derivatives with the variable Riesz-Feller derivatives. The problem is solved by an explicit finite difference method. Finally, simulatio...

Let $p:Xlo B$ be a locally trivial principal G-bundle and $wt{p}:wt{X}lo B$ be a locally trivial principal $wt{G}$-bundle. In this paper, by using the structure of principal bundles according to transition functions, we show that $wt{G}$ is a covering group of $G$ if and only if $wt{X}$ is a covering space of $X$. Then we conclude that a topological space $X$ with non-simply connected universal...

Following the approach of Chui and Quak, we investigate semi-orthogonal spline wavelets on the unit interval [0, 1]. We give a slightly different construction of boundary wavelets. As a result, we are able to prove that the inner wavelets and the newly constructed boundary wavelets together constitute a Riesz basis for the wavelet space at each level with the Riesz bounds being level-independen...